Problem: Solve for $x$ and $y$ using elimination. ${x+3y = 27}$ ${3x+5y = 57}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-3$ ${-3x-9y = -81}$ $3x+5y = 57$ Add the top and bottom equations together. $-4y = -24$ $\dfrac{-4y}{{-4}} = \dfrac{-24}{{-4}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {x+3y = 27}\thinspace$ to find $x$ ${x + 3}{(6)}{= 27}$ $x+18 = 27$ $x+18{-18} = 27{-18}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {3x+5y = 57}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(6)}{= 57}$ ${x = 9}$